This work establishes that universality in nonlinear transport systems is not global, but constraint-dependent. Building on prior ΔΦ formulations of optimal coupling and attractor stability, this study demonstrates that a topology-invariant optimal coupling (p*) emerges only within a specific region of parameter space defined by saturation and suppression.Across grid, small-world, and random networks, systematic sweeps reveal that optimal coupling converges to a narrow band (p* ≈ 0.10–0.11) with minimal variance—but only within a bounded regime. Outside this region, optimal behavior diverges and becomes topology-dependent, indicating a breakdown of universality.The results introduce a new class of invariant: constraint-bounded universality, in which agreement across fundamentally different structures is enforced not by the system itself, but by the constraints under which it operates. This reframes universality as a phase-dependent phenomenon and provides a unifying explanation for efficient transport in biological and distributed systems.The findings are computationally derived, reproducible, and directly testable across synthetic and physical transport networks.
Thomas S. Mitchell (Sun,) studied this question.